Question

`Sin theta = cos theta` is possible, where `theta` is an angle in a triangle. Is this true or false?

Answer 1

This is true. See below for proof.

Explanation:

Consider the classic `45˚, 45˚, 90˚` triangle, as shown in the following diagram.

The definition of `sin` is opposite/hypotenuse.

The definition of `cos` is adjacent/hypotenuse.

In the vast majority of situations, the side adjacent `theta` will be different than the side opposite `theta`. However, in the extremely particular case that the opposite and adjacent sides are the same, `sintheta` and `costheta` will be equal, because these functions measure the relationships between sides, and if these relationships are equal, the functions will be equal in value.

Hopefully this helps!

Answer 2

True.

Explanation:

If sin x = cos x, then tan x = 1 --> x = pi/4.
The answer is true, when a right triangle has 2 angles of (pi/4)